Properties

Label 882.2.e.n.655.1
Level $882$
Weight $2$
Character 882.655
Analytic conductor $7.043$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 655.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.655
Dual form 882.2.e.n.373.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.724745 - 1.57313i) q^{3} +1.00000 q^{4} +(1.72474 - 2.98735i) q^{5} +(-0.724745 - 1.57313i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.724745 - 1.57313i) q^{3} +1.00000 q^{4} +(1.72474 - 2.98735i) q^{5} +(-0.724745 - 1.57313i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +(1.72474 - 2.98735i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-0.724745 - 1.57313i) q^{12} +(-2.44949 - 4.24264i) q^{13} +(-5.94949 - 0.548188i) q^{15} +1.00000 q^{16} +(1.00000 - 1.73205i) q^{17} +(-1.94949 + 2.28024i) q^{18} +(3.72474 + 6.45145i) q^{19} +(1.72474 - 2.98735i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.724745 - 1.57313i) q^{24} +(-3.44949 - 5.97469i) q^{25} +(-2.44949 - 4.24264i) q^{26} +(5.00000 + 1.41421i) q^{27} +(-1.44949 + 2.51059i) q^{29} +(-5.94949 - 0.548188i) q^{30} -6.00000 q^{31} +1.00000 q^{32} +(-2.00000 + 2.82843i) q^{33} +(1.00000 - 1.73205i) q^{34} +(-1.94949 + 2.28024i) q^{36} +(3.89898 + 6.75323i) q^{37} +(3.72474 + 6.45145i) q^{38} +(-4.89898 + 6.92820i) q^{39} +(1.72474 - 2.98735i) q^{40} +(-4.89898 - 8.48528i) q^{41} +(1.44949 - 2.51059i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(3.44949 + 9.75663i) q^{45} +(0.500000 - 0.866025i) q^{46} +9.79796 q^{47} +(-0.724745 - 1.57313i) q^{48} +(-3.44949 - 5.97469i) q^{50} +(-3.44949 - 0.317837i) q^{51} +(-2.44949 - 4.24264i) q^{52} +(0.550510 - 0.953512i) q^{53} +(5.00000 + 1.41421i) q^{54} -6.89898 q^{55} +(7.44949 - 10.5352i) q^{57} +(-1.44949 + 2.51059i) q^{58} +2.00000 q^{59} +(-5.94949 - 0.548188i) q^{60} -11.4495 q^{61} -6.00000 q^{62} +1.00000 q^{64} -16.8990 q^{65} +(-2.00000 + 2.82843i) q^{66} -3.10102 q^{67} +(1.00000 - 1.73205i) q^{68} +(-1.72474 - 0.158919i) q^{69} +9.89898 q^{71} +(-1.94949 + 2.28024i) q^{72} +(1.44949 - 2.51059i) q^{73} +(3.89898 + 6.75323i) q^{74} +(-6.89898 + 9.75663i) q^{75} +(3.72474 + 6.45145i) q^{76} +(-4.89898 + 6.92820i) q^{78} +7.89898 q^{79} +(1.72474 - 2.98735i) q^{80} +(-1.39898 - 8.89060i) q^{81} +(-4.89898 - 8.48528i) q^{82} +(1.00000 - 1.73205i) q^{83} +(-3.44949 - 5.97469i) q^{85} +(1.44949 - 2.51059i) q^{86} +(5.00000 + 0.460702i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(-3.55051 - 6.14966i) q^{89} +(3.44949 + 9.75663i) q^{90} +(0.500000 - 0.866025i) q^{92} +(4.34847 + 9.43879i) q^{93} +9.79796 q^{94} +25.6969 q^{95} +(-0.724745 - 1.57313i) q^{96} +(-3.44949 + 5.97469i) q^{97} +(5.89898 + 1.09638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 2q^{3} + 4q^{4} + 2q^{5} + 2q^{6} + 4q^{8} + 2q^{9} + O(q^{10}) \) \( 4q + 4q^{2} + 2q^{3} + 4q^{4} + 2q^{5} + 2q^{6} + 4q^{8} + 2q^{9} + 2q^{10} - 4q^{11} + 2q^{12} - 14q^{15} + 4q^{16} + 4q^{17} + 2q^{18} + 10q^{19} + 2q^{20} - 4q^{22} + 2q^{23} + 2q^{24} - 4q^{25} + 20q^{27} + 4q^{29} - 14q^{30} - 24q^{31} + 4q^{32} - 8q^{33} + 4q^{34} + 2q^{36} - 4q^{37} + 10q^{38} + 2q^{40} - 4q^{43} - 4q^{44} + 4q^{45} + 2q^{46} + 2q^{48} - 4q^{50} - 4q^{51} + 12q^{53} + 20q^{54} - 8q^{55} + 20q^{57} + 4q^{58} + 8q^{59} - 14q^{60} - 36q^{61} - 24q^{62} + 4q^{64} - 48q^{65} - 8q^{66} - 32q^{67} + 4q^{68} - 2q^{69} + 20q^{71} + 2q^{72} - 4q^{73} - 4q^{74} - 8q^{75} + 10q^{76} + 12q^{79} + 2q^{80} + 14q^{81} + 4q^{83} - 4q^{85} - 4q^{86} + 20q^{87} - 4q^{88} - 24q^{89} + 4q^{90} + 2q^{92} - 12q^{93} + 44q^{95} + 2q^{96} - 4q^{97} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.724745 1.57313i −0.418432 0.908248i
\(4\) 1.00000 0.500000
\(5\) 1.72474 2.98735i 0.771329 1.33598i −0.165505 0.986209i \(-0.552925\pi\)
0.936835 0.349773i \(-0.113741\pi\)
\(6\) −0.724745 1.57313i −0.295876 0.642229i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −1.94949 + 2.28024i −0.649830 + 0.760080i
\(10\) 1.72474 2.98735i 0.545412 0.944682i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) −0.724745 1.57313i −0.209216 0.454124i
\(13\) −2.44949 4.24264i −0.679366 1.17670i −0.975172 0.221449i \(-0.928921\pi\)
0.295806 0.955248i \(-0.404412\pi\)
\(14\) 0 0
\(15\) −5.94949 0.548188i −1.53615 0.141542i
\(16\) 1.00000 0.250000
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) −1.94949 + 2.28024i −0.459499 + 0.537457i
\(19\) 3.72474 + 6.45145i 0.854515 + 1.48006i 0.877094 + 0.480318i \(0.159479\pi\)
−0.0225791 + 0.999745i \(0.507188\pi\)
\(20\) 1.72474 2.98735i 0.385665 0.667991i
\(21\) 0 0
\(22\) −1.00000 1.73205i −0.213201 0.369274i
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) −0.724745 1.57313i −0.147938 0.321114i
\(25\) −3.44949 5.97469i −0.689898 1.19494i
\(26\) −2.44949 4.24264i −0.480384 0.832050i
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) 0 0
\(29\) −1.44949 + 2.51059i −0.269163 + 0.466205i −0.968646 0.248445i \(-0.920081\pi\)
0.699483 + 0.714650i \(0.253414\pi\)
\(30\) −5.94949 0.548188i −1.08622 0.100085i
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.00000 + 2.82843i −0.348155 + 0.492366i
\(34\) 1.00000 1.73205i 0.171499 0.297044i
\(35\) 0 0
\(36\) −1.94949 + 2.28024i −0.324915 + 0.380040i
\(37\) 3.89898 + 6.75323i 0.640988 + 1.11022i 0.985213 + 0.171337i \(0.0548086\pi\)
−0.344224 + 0.938887i \(0.611858\pi\)
\(38\) 3.72474 + 6.45145i 0.604233 + 1.04656i
\(39\) −4.89898 + 6.92820i −0.784465 + 1.10940i
\(40\) 1.72474 2.98735i 0.272706 0.472341i
\(41\) −4.89898 8.48528i −0.765092 1.32518i −0.940198 0.340629i \(-0.889360\pi\)
0.175106 0.984550i \(-0.443973\pi\)
\(42\) 0 0
\(43\) 1.44949 2.51059i 0.221045 0.382861i −0.734080 0.679062i \(-0.762387\pi\)
0.955126 + 0.296201i \(0.0957199\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) 3.44949 + 9.75663i 0.514220 + 1.45443i
\(46\) 0.500000 0.866025i 0.0737210 0.127688i
\(47\) 9.79796 1.42918 0.714590 0.699544i \(-0.246613\pi\)
0.714590 + 0.699544i \(0.246613\pi\)
\(48\) −0.724745 1.57313i −0.104608 0.227062i
\(49\) 0 0
\(50\) −3.44949 5.97469i −0.487832 0.844949i
\(51\) −3.44949 0.317837i −0.483025 0.0445061i
\(52\) −2.44949 4.24264i −0.339683 0.588348i
\(53\) 0.550510 0.953512i 0.0756184 0.130975i −0.825737 0.564056i \(-0.809240\pi\)
0.901355 + 0.433081i \(0.142574\pi\)
\(54\) 5.00000 + 1.41421i 0.680414 + 0.192450i
\(55\) −6.89898 −0.930258
\(56\) 0 0
\(57\) 7.44949 10.5352i 0.986709 1.39542i
\(58\) −1.44949 + 2.51059i −0.190327 + 0.329657i
\(59\) 2.00000 0.260378 0.130189 0.991489i \(-0.458442\pi\)
0.130189 + 0.991489i \(0.458442\pi\)
\(60\) −5.94949 0.548188i −0.768076 0.0707708i
\(61\) −11.4495 −1.46596 −0.732978 0.680252i \(-0.761870\pi\)
−0.732978 + 0.680252i \(0.761870\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −16.8990 −2.09606
\(66\) −2.00000 + 2.82843i −0.246183 + 0.348155i
\(67\) −3.10102 −0.378850 −0.189425 0.981895i \(-0.560662\pi\)
−0.189425 + 0.981895i \(0.560662\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) −1.72474 0.158919i −0.207635 0.0191316i
\(70\) 0 0
\(71\) 9.89898 1.17479 0.587396 0.809299i \(-0.300153\pi\)
0.587396 + 0.809299i \(0.300153\pi\)
\(72\) −1.94949 + 2.28024i −0.229750 + 0.268729i
\(73\) 1.44949 2.51059i 0.169650 0.293842i −0.768647 0.639673i \(-0.779070\pi\)
0.938297 + 0.345831i \(0.112403\pi\)
\(74\) 3.89898 + 6.75323i 0.453247 + 0.785047i
\(75\) −6.89898 + 9.75663i −0.796626 + 1.12660i
\(76\) 3.72474 + 6.45145i 0.427258 + 0.740032i
\(77\) 0 0
\(78\) −4.89898 + 6.92820i −0.554700 + 0.784465i
\(79\) 7.89898 0.888705 0.444352 0.895852i \(-0.353434\pi\)
0.444352 + 0.895852i \(0.353434\pi\)
\(80\) 1.72474 2.98735i 0.192832 0.333995i
\(81\) −1.39898 8.89060i −0.155442 0.987845i
\(82\) −4.89898 8.48528i −0.541002 0.937043i
\(83\) 1.00000 1.73205i 0.109764 0.190117i −0.805910 0.592037i \(-0.798324\pi\)
0.915675 + 0.401920i \(0.131657\pi\)
\(84\) 0 0
\(85\) −3.44949 5.97469i −0.374150 0.648046i
\(86\) 1.44949 2.51059i 0.156302 0.270724i
\(87\) 5.00000 + 0.460702i 0.536056 + 0.0493924i
\(88\) −1.00000 1.73205i −0.106600 0.184637i
\(89\) −3.55051 6.14966i −0.376353 0.651863i 0.614175 0.789170i \(-0.289489\pi\)
−0.990529 + 0.137307i \(0.956155\pi\)
\(90\) 3.44949 + 9.75663i 0.363608 + 1.02844i
\(91\) 0 0
\(92\) 0.500000 0.866025i 0.0521286 0.0902894i
\(93\) 4.34847 + 9.43879i 0.450915 + 0.978757i
\(94\) 9.79796 1.01058
\(95\) 25.6969 2.63645
\(96\) −0.724745 1.57313i −0.0739690 0.160557i
\(97\) −3.44949 + 5.97469i −0.350243 + 0.606638i −0.986292 0.165011i \(-0.947234\pi\)
0.636049 + 0.771649i \(0.280568\pi\)
\(98\) 0 0
\(99\) 5.89898 + 1.09638i 0.592870 + 0.110190i
\(100\) −3.44949 5.97469i −0.344949 0.597469i
\(101\) 3.62372 + 6.27647i 0.360574 + 0.624533i 0.988055 0.154099i \(-0.0492475\pi\)
−0.627481 + 0.778632i \(0.715914\pi\)
\(102\) −3.44949 0.317837i −0.341550 0.0314706i
\(103\) 7.00000 12.1244i 0.689730 1.19465i −0.282194 0.959357i \(-0.591062\pi\)
0.971925 0.235291i \(-0.0756043\pi\)
\(104\) −2.44949 4.24264i −0.240192 0.416025i
\(105\) 0 0
\(106\) 0.550510 0.953512i 0.0534703 0.0926132i
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) 5.00000 + 1.41421i 0.481125 + 0.136083i
\(109\) 8.34847 14.4600i 0.799638 1.38501i −0.120213 0.992748i \(-0.538358\pi\)
0.919852 0.392266i \(-0.128309\pi\)
\(110\) −6.89898 −0.657792
\(111\) 7.79796 11.0280i 0.740150 1.04673i
\(112\) 0 0
\(113\) 7.94949 + 13.7689i 0.747825 + 1.29527i 0.948863 + 0.315688i \(0.102235\pi\)
−0.201038 + 0.979583i \(0.564431\pi\)
\(114\) 7.44949 10.5352i 0.697709 0.986709i
\(115\) −1.72474 2.98735i −0.160833 0.278571i
\(116\) −1.44949 + 2.51059i −0.134582 + 0.233102i
\(117\) 14.4495 + 2.68556i 1.33586 + 0.248280i
\(118\) 2.00000 0.184115
\(119\) 0 0
\(120\) −5.94949 0.548188i −0.543112 0.0500425i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −11.4495 −1.03659
\(123\) −9.79796 + 13.8564i −0.883452 + 1.24939i
\(124\) −6.00000 −0.538816
\(125\) −6.55051 −0.585895
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.00000 0.460702i −0.440225 0.0405625i
\(130\) −16.8990 −1.48214
\(131\) −6.72474 + 11.6476i −0.587544 + 1.01766i 0.407009 + 0.913424i \(0.366572\pi\)
−0.994553 + 0.104232i \(0.966762\pi\)
\(132\) −2.00000 + 2.82843i −0.174078 + 0.246183i
\(133\) 0 0
\(134\) −3.10102 −0.267887
\(135\) 12.8485 12.4976i 1.10582 1.07562i
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) 5.89898 + 10.2173i 0.503984 + 0.872926i 0.999989 + 0.00460626i \(0.00146622\pi\)
−0.496006 + 0.868319i \(0.665200\pi\)
\(138\) −1.72474 0.158919i −0.146820 0.0135281i
\(139\) 4.72474 + 8.18350i 0.400748 + 0.694115i 0.993816 0.111037i \(-0.0354171\pi\)
−0.593069 + 0.805152i \(0.702084\pi\)
\(140\) 0 0
\(141\) −7.10102 15.4135i −0.598014 1.29805i
\(142\) 9.89898 0.830704
\(143\) −4.89898 + 8.48528i −0.409673 + 0.709575i
\(144\) −1.94949 + 2.28024i −0.162457 + 0.190020i
\(145\) 5.00000 + 8.66025i 0.415227 + 0.719195i
\(146\) 1.44949 2.51059i 0.119961 0.207778i
\(147\) 0 0
\(148\) 3.89898 + 6.75323i 0.320494 + 0.555112i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) −6.89898 + 9.75663i −0.563299 + 0.796626i
\(151\) 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i \(-0.101452\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(152\) 3.72474 + 6.45145i 0.302117 + 0.523281i
\(153\) 2.00000 + 5.65685i 0.161690 + 0.457330i
\(154\) 0 0
\(155\) −10.3485 + 17.9241i −0.831209 + 1.43970i
\(156\) −4.89898 + 6.92820i −0.392232 + 0.554700i
\(157\) −6.34847 −0.506663 −0.253332 0.967380i \(-0.581526\pi\)
−0.253332 + 0.967380i \(0.581526\pi\)
\(158\) 7.89898 0.628409
\(159\) −1.89898 0.174973i −0.150599 0.0138762i
\(160\) 1.72474 2.98735i 0.136353 0.236170i
\(161\) 0 0
\(162\) −1.39898 8.89060i −0.109914 0.698512i
\(163\) 0.101021 + 0.174973i 0.00791254 + 0.0137049i 0.869955 0.493132i \(-0.164148\pi\)
−0.862042 + 0.506837i \(0.830815\pi\)
\(164\) −4.89898 8.48528i −0.382546 0.662589i
\(165\) 5.00000 + 10.8530i 0.389249 + 0.844905i
\(166\) 1.00000 1.73205i 0.0776151 0.134433i
\(167\) 9.34847 + 16.1920i 0.723406 + 1.25298i 0.959627 + 0.281277i \(0.0907579\pi\)
−0.236220 + 0.971700i \(0.575909\pi\)
\(168\) 0 0
\(169\) −5.50000 + 9.52628i −0.423077 + 0.732791i
\(170\) −3.44949 5.97469i −0.264564 0.458238i
\(171\) −21.9722 4.08372i −1.68026 0.312290i
\(172\) 1.44949 2.51059i 0.110523 0.191431i
\(173\) 12.8990 0.980691 0.490346 0.871528i \(-0.336871\pi\)
0.490346 + 0.871528i \(0.336871\pi\)
\(174\) 5.00000 + 0.460702i 0.379049 + 0.0349257i
\(175\) 0 0
\(176\) −1.00000 1.73205i −0.0753778 0.130558i
\(177\) −1.44949 3.14626i −0.108950 0.236488i
\(178\) −3.55051 6.14966i −0.266122 0.460937i
\(179\) 4.34847 7.53177i 0.325020 0.562951i −0.656497 0.754329i \(-0.727962\pi\)
0.981516 + 0.191378i \(0.0612957\pi\)
\(180\) 3.44949 + 9.75663i 0.257110 + 0.727216i
\(181\) −4.34847 −0.323219 −0.161610 0.986855i \(-0.551669\pi\)
−0.161610 + 0.986855i \(0.551669\pi\)
\(182\) 0 0
\(183\) 8.29796 + 18.0116i 0.613403 + 1.33145i
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) 26.8990 1.97765
\(186\) 4.34847 + 9.43879i 0.318845 + 0.692086i
\(187\) −4.00000 −0.292509
\(188\) 9.79796 0.714590
\(189\) 0 0
\(190\) 25.6969 1.86425
\(191\) 13.8990 1.00569 0.502847 0.864375i \(-0.332286\pi\)
0.502847 + 0.864375i \(0.332286\pi\)
\(192\) −0.724745 1.57313i −0.0523040 0.113531i
\(193\) −8.10102 −0.583124 −0.291562 0.956552i \(-0.594175\pi\)
−0.291562 + 0.956552i \(0.594175\pi\)
\(194\) −3.44949 + 5.97469i −0.247659 + 0.428958i
\(195\) 12.2474 + 26.5843i 0.877058 + 1.90374i
\(196\) 0 0
\(197\) −12.6969 −0.904619 −0.452310 0.891861i \(-0.649400\pi\)
−0.452310 + 0.891861i \(0.649400\pi\)
\(198\) 5.89898 + 1.09638i 0.419222 + 0.0779161i
\(199\) 3.44949 5.97469i 0.244528 0.423535i −0.717471 0.696588i \(-0.754700\pi\)
0.961999 + 0.273054i \(0.0880337\pi\)
\(200\) −3.44949 5.97469i −0.243916 0.422474i
\(201\) 2.24745 + 4.87832i 0.158523 + 0.344090i
\(202\) 3.62372 + 6.27647i 0.254964 + 0.441611i
\(203\) 0 0
\(204\) −3.44949 0.317837i −0.241513 0.0222531i
\(205\) −33.7980 −2.36055
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) 1.00000 + 2.82843i 0.0695048 + 0.196589i
\(208\) −2.44949 4.24264i −0.169842 0.294174i
\(209\) 7.44949 12.9029i 0.515292 0.892512i
\(210\) 0 0
\(211\) −1.55051 2.68556i −0.106742 0.184882i 0.807707 0.589584i \(-0.200708\pi\)
−0.914448 + 0.404703i \(0.867375\pi\)
\(212\) 0.550510 0.953512i 0.0378092 0.0654875i
\(213\) −7.17423 15.5724i −0.491570 1.06700i
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) −5.00000 8.66025i −0.340997 0.590624i
\(216\) 5.00000 + 1.41421i 0.340207 + 0.0962250i
\(217\) 0 0
\(218\) 8.34847 14.4600i 0.565430 0.979353i
\(219\) −5.00000 0.460702i −0.337869 0.0311313i
\(220\) −6.89898 −0.465129
\(221\) −9.79796 −0.659082
\(222\) 7.79796 11.0280i 0.523365 0.740150i
\(223\) −10.4495 + 18.0990i −0.699750 + 1.21200i 0.268804 + 0.963195i \(0.413372\pi\)
−0.968553 + 0.248807i \(0.919962\pi\)
\(224\) 0 0
\(225\) 20.3485 + 3.78194i 1.35656 + 0.252129i
\(226\) 7.94949 + 13.7689i 0.528792 + 0.915895i
\(227\) −0.275255 0.476756i −0.0182693 0.0316434i 0.856746 0.515738i \(-0.172482\pi\)
−0.875016 + 0.484095i \(0.839149\pi\)
\(228\) 7.44949 10.5352i 0.493355 0.697709i
\(229\) −11.6237 + 20.1329i −0.768117 + 1.33042i 0.170465 + 0.985364i \(0.445473\pi\)
−0.938583 + 0.345055i \(0.887860\pi\)
\(230\) −1.72474 2.98735i −0.113726 0.196980i
\(231\) 0 0
\(232\) −1.44949 + 2.51059i −0.0951637 + 0.164828i
\(233\) 3.50000 + 6.06218i 0.229293 + 0.397146i 0.957599 0.288106i \(-0.0930254\pi\)
−0.728306 + 0.685252i \(0.759692\pi\)
\(234\) 14.4495 + 2.68556i 0.944593 + 0.175561i
\(235\) 16.8990 29.2699i 1.10237 1.90936i
\(236\) 2.00000 0.130189
\(237\) −5.72474 12.4261i −0.371862 0.807164i
\(238\) 0 0
\(239\) 6.39898 + 11.0834i 0.413916 + 0.716923i 0.995314 0.0966962i \(-0.0308275\pi\)
−0.581398 + 0.813619i \(0.697494\pi\)
\(240\) −5.94949 0.548188i −0.384038 0.0353854i
\(241\) −4.44949 7.70674i −0.286617 0.496435i 0.686383 0.727240i \(-0.259197\pi\)
−0.973000 + 0.230805i \(0.925864\pi\)
\(242\) 3.50000 6.06218i 0.224989 0.389692i
\(243\) −12.9722 + 8.64420i −0.832167 + 0.554526i
\(244\) −11.4495 −0.732978
\(245\) 0 0
\(246\) −9.79796 + 13.8564i −0.624695 + 0.883452i
\(247\) 18.2474 31.6055i 1.16106 2.01101i
\(248\) −6.00000 −0.381000
\(249\) −3.44949 0.317837i −0.218603 0.0201421i
\(250\) −6.55051 −0.414291
\(251\) −12.5505 −0.792181 −0.396091 0.918211i \(-0.629633\pi\)
−0.396091 + 0.918211i \(0.629633\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) −3.00000 −0.188237
\(255\) −6.89898 + 9.75663i −0.432031 + 0.610984i
\(256\) 1.00000 0.0625000
\(257\) 13.8990 24.0737i 0.866995 1.50168i 0.00194150 0.999998i \(-0.499382\pi\)
0.865053 0.501680i \(-0.167285\pi\)
\(258\) −5.00000 0.460702i −0.311286 0.0286820i
\(259\) 0 0
\(260\) −16.8990 −1.04803
\(261\) −2.89898 8.19955i −0.179442 0.507540i
\(262\) −6.72474 + 11.6476i −0.415456 + 0.719591i
\(263\) −8.05051 13.9439i −0.496416 0.859817i 0.503576 0.863951i \(-0.332017\pi\)
−0.999991 + 0.00413383i \(0.998684\pi\)
\(264\) −2.00000 + 2.82843i −0.123091 + 0.174078i
\(265\) −1.89898 3.28913i −0.116653 0.202050i
\(266\) 0 0
\(267\) −7.10102 + 10.0424i −0.434575 + 0.614582i
\(268\) −3.10102 −0.189425
\(269\) −1.82577 + 3.16232i −0.111319 + 0.192810i −0.916302 0.400487i \(-0.868841\pi\)
0.804983 + 0.593297i \(0.202174\pi\)
\(270\) 12.8485 12.4976i 0.781933 0.760578i
\(271\) 8.44949 + 14.6349i 0.513270 + 0.889010i 0.999882 + 0.0153912i \(0.00489937\pi\)
−0.486612 + 0.873618i \(0.661767\pi\)
\(272\) 1.00000 1.73205i 0.0606339 0.105021i
\(273\) 0 0
\(274\) 5.89898 + 10.2173i 0.356370 + 0.617252i
\(275\) −6.89898 + 11.9494i −0.416024 + 0.720575i
\(276\) −1.72474 0.158919i −0.103817 0.00956578i
\(277\) −5.34847 9.26382i −0.321358 0.556609i 0.659410 0.751783i \(-0.270806\pi\)
−0.980769 + 0.195174i \(0.937473\pi\)
\(278\) 4.72474 + 8.18350i 0.283371 + 0.490814i
\(279\) 11.6969 13.6814i 0.700277 0.819086i
\(280\) 0 0
\(281\) 9.50000 16.4545i 0.566722 0.981592i −0.430165 0.902750i \(-0.641545\pi\)
0.996887 0.0788417i \(-0.0251222\pi\)
\(282\) −7.10102 15.4135i −0.422860 0.917860i
\(283\) 20.5505 1.22160 0.610801 0.791785i \(-0.290848\pi\)
0.610801 + 0.791785i \(0.290848\pi\)
\(284\) 9.89898 0.587396
\(285\) −18.6237 40.4247i −1.10317 2.39455i
\(286\) −4.89898 + 8.48528i −0.289683 + 0.501745i
\(287\) 0 0
\(288\) −1.94949 + 2.28024i −0.114875 + 0.134364i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 5.00000 + 8.66025i 0.293610 + 0.508548i
\(291\) 11.8990 + 1.09638i 0.697531 + 0.0642707i
\(292\) 1.44949 2.51059i 0.0848250 0.146921i
\(293\) 13.6237 + 23.5970i 0.795906 + 1.37855i 0.922262 + 0.386565i \(0.126339\pi\)
−0.126356 + 0.991985i \(0.540328\pi\)
\(294\) 0 0
\(295\) 3.44949 5.97469i 0.200837 0.347860i
\(296\) 3.89898 + 6.75323i 0.226624 + 0.392524i
\(297\) −2.55051 10.0745i −0.147996 0.584580i
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) −4.89898 −0.283315
\(300\) −6.89898 + 9.75663i −0.398313 + 0.563299i
\(301\) 0 0
\(302\) 2.50000 + 4.33013i 0.143859 + 0.249171i
\(303\) 7.24745 10.2494i 0.416355 0.588815i
\(304\) 3.72474 + 6.45145i 0.213629 + 0.370016i
\(305\) −19.7474 + 34.2036i −1.13074 + 1.95849i
\(306\) 2.00000 + 5.65685i 0.114332 + 0.323381i
\(307\) −0.752551 −0.0429504 −0.0214752 0.999769i \(-0.506836\pi\)
−0.0214752 + 0.999769i \(0.506836\pi\)
\(308\) 0 0
\(309\) −24.1464 2.22486i −1.37364 0.126568i
\(310\) −10.3485 + 17.9241i −0.587754 + 1.01802i
\(311\) −1.30306 −0.0738898 −0.0369449 0.999317i \(-0.511763\pi\)
−0.0369449 + 0.999317i \(0.511763\pi\)
\(312\) −4.89898 + 6.92820i −0.277350 + 0.392232i
\(313\) −24.6969 −1.39595 −0.697977 0.716120i \(-0.745916\pi\)
−0.697977 + 0.716120i \(0.745916\pi\)
\(314\) −6.34847 −0.358265
\(315\) 0 0
\(316\) 7.89898 0.444352
\(317\) −8.69694 −0.488469 −0.244234 0.969716i \(-0.578537\pi\)
−0.244234 + 0.969716i \(0.578537\pi\)
\(318\) −1.89898 0.174973i −0.106489 0.00981198i
\(319\) 5.79796 0.324623
\(320\) 1.72474 2.98735i 0.0964162 0.166998i
\(321\) 12.0000 16.9706i 0.669775 0.947204i
\(322\) 0 0
\(323\) 14.8990 0.829001
\(324\) −1.39898 8.89060i −0.0777211 0.493922i
\(325\) −16.8990 + 29.2699i −0.937387 + 1.62360i
\(326\) 0.101021 + 0.174973i 0.00559501 + 0.00969084i
\(327\) −28.7980 2.65345i −1.59253 0.146736i
\(328\) −4.89898 8.48528i −0.270501 0.468521i
\(329\) 0 0
\(330\) 5.00000 + 10.8530i 0.275241 + 0.597438i
\(331\) −24.6969 −1.35747 −0.678733 0.734385i \(-0.737471\pi\)
−0.678733 + 0.734385i \(0.737471\pi\)
\(332\) 1.00000 1.73205i 0.0548821 0.0950586i
\(333\) −23.0000 4.27475i −1.26039 0.234255i
\(334\) 9.34847 + 16.1920i 0.511525 + 0.885988i
\(335\) −5.34847 + 9.26382i −0.292218 + 0.506137i
\(336\) 0 0
\(337\) −17.6969 30.6520i −0.964014 1.66972i −0.712242 0.701934i \(-0.752320\pi\)
−0.251772 0.967787i \(-0.581013\pi\)
\(338\) −5.50000 + 9.52628i −0.299161 + 0.518161i
\(339\) 15.8990 22.4846i 0.863514 1.22119i
\(340\) −3.44949 5.97469i −0.187075 0.324023i
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) −21.9722 4.08372i −1.18812 0.220822i
\(343\) 0 0
\(344\) 1.44949 2.51059i 0.0781512 0.135362i
\(345\) −3.44949 + 4.87832i −0.185714 + 0.262640i
\(346\) 12.8990 0.693453
\(347\) −19.5959 −1.05196 −0.525982 0.850496i \(-0.676302\pi\)
−0.525982 + 0.850496i \(0.676302\pi\)
\(348\) 5.00000 + 0.460702i 0.268028 + 0.0246962i
\(349\) 10.4495 18.0990i 0.559348 0.968820i −0.438203 0.898876i \(-0.644385\pi\)
0.997551 0.0699435i \(-0.0222819\pi\)
\(350\) 0 0
\(351\) −6.24745 24.6773i −0.333464 1.31718i
\(352\) −1.00000 1.73205i −0.0533002 0.0923186i
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) −1.44949 3.14626i −0.0770395 0.167222i
\(355\) 17.0732 29.5717i 0.906152 1.56950i
\(356\) −3.55051 6.14966i −0.188177 0.325932i
\(357\) 0 0
\(358\) 4.34847 7.53177i 0.229824 0.398066i
\(359\) −5.39898 9.35131i −0.284947 0.493543i 0.687649 0.726043i \(-0.258643\pi\)
−0.972596 + 0.232500i \(0.925309\pi\)
\(360\) 3.44949 + 9.75663i 0.181804 + 0.514220i
\(361\) −18.2474 + 31.6055i −0.960392 + 1.66345i
\(362\) −4.34847 −0.228550
\(363\) −12.0732 1.11243i −0.633679 0.0583875i
\(364\) 0 0
\(365\) −5.00000 8.66025i −0.261712 0.453298i
\(366\) 8.29796 + 18.0116i 0.433741 + 0.941479i
\(367\) 2.89898 + 5.02118i 0.151325 + 0.262103i 0.931715 0.363190i \(-0.118313\pi\)
−0.780389 + 0.625294i \(0.784979\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) 28.8990 + 5.37113i 1.50442 + 0.279610i
\(370\) 26.8990 1.39841
\(371\) 0 0
\(372\) 4.34847 + 9.43879i 0.225458 + 0.489379i
\(373\) −1.44949 + 2.51059i −0.0750517 + 0.129993i −0.901109 0.433593i \(-0.857246\pi\)
0.826057 + 0.563587i \(0.190579\pi\)
\(374\) −4.00000 −0.206835
\(375\) 4.74745 + 10.3048i 0.245157 + 0.532139i
\(376\) 9.79796 0.505291
\(377\) 14.2020 0.731442
\(378\) 0 0
\(379\) −26.4949 −1.36095 −0.680476 0.732771i \(-0.738227\pi\)
−0.680476 + 0.732771i \(0.738227\pi\)
\(380\) 25.6969 1.31823
\(381\) 2.17423 + 4.71940i 0.111389 + 0.241782i
\(382\) 13.8990 0.711134
\(383\) 3.44949 5.97469i 0.176261 0.305292i −0.764336 0.644818i \(-0.776933\pi\)
0.940597 + 0.339526i \(0.110266\pi\)
\(384\) −0.724745 1.57313i −0.0369845 0.0802786i
\(385\) 0 0
\(386\) −8.10102 −0.412331
\(387\) 2.89898 + 8.19955i 0.147363 + 0.416807i
\(388\) −3.44949 + 5.97469i −0.175121 + 0.303319i
\(389\) 7.55051 + 13.0779i 0.382826 + 0.663074i 0.991465 0.130373i \(-0.0416175\pi\)
−0.608639 + 0.793447i \(0.708284\pi\)
\(390\) 12.2474 + 26.5843i 0.620174 + 1.34615i
\(391\) −1.00000 1.73205i −0.0505722 0.0875936i
\(392\) 0 0
\(393\) 23.1969 + 2.13737i 1.17013 + 0.107816i
\(394\) −12.6969 −0.639663
\(395\) 13.6237 23.5970i 0.685484 1.18729i
\(396\) 5.89898 + 1.09638i 0.296435 + 0.0550950i
\(397\) 4.65153 + 8.05669i 0.233454 + 0.404354i 0.958822 0.284007i \(-0.0916640\pi\)
−0.725369 + 0.688361i \(0.758331\pi\)
\(398\) 3.44949 5.97469i 0.172907 0.299484i
\(399\) 0 0
\(400\) −3.44949 5.97469i −0.172474 0.298735i
\(401\) 5.05051 8.74774i 0.252210 0.436841i −0.711924 0.702257i \(-0.752176\pi\)
0.964134 + 0.265416i \(0.0855091\pi\)
\(402\) 2.24745 + 4.87832i 0.112093 + 0.243308i
\(403\) 14.6969 + 25.4558i 0.732107 + 1.26805i
\(404\) 3.62372 + 6.27647i 0.180287 + 0.312266i
\(405\) −28.9722 11.1548i −1.43964 0.554286i
\(406\) 0 0
\(407\) 7.79796 13.5065i 0.386530 0.669490i
\(408\) −3.44949 0.317837i −0.170775 0.0157353i
\(409\) −5.79796 −0.286691 −0.143345 0.989673i \(-0.545786\pi\)
−0.143345 + 0.989673i \(0.545786\pi\)
\(410\) −33.7980 −1.66916
\(411\) 11.7980 16.6848i 0.581950 0.823002i
\(412\) 7.00000 12.1244i 0.344865 0.597324i
\(413\) 0 0
\(414\) 1.00000 + 2.82843i 0.0491473 + 0.139010i
\(415\) −3.44949 5.97469i −0.169329 0.293286i
\(416\) −2.44949 4.24264i −0.120096 0.208013i
\(417\) 9.44949 13.3636i 0.462744 0.654418i
\(418\) 7.44949 12.9029i 0.364366 0.631101i
\(419\) 12.2753 + 21.2614i 0.599685 + 1.03869i 0.992867 + 0.119225i \(0.0380410\pi\)
−0.393182 + 0.919461i \(0.628626\pi\)
\(420\) 0 0
\(421\) −6.55051 + 11.3458i −0.319252 + 0.552961i −0.980332 0.197354i \(-0.936765\pi\)
0.661080 + 0.750316i \(0.270098\pi\)
\(422\) −1.55051 2.68556i −0.0754777 0.130731i
\(423\) −19.1010 + 22.3417i −0.928723 + 1.08629i
\(424\) 0.550510 0.953512i 0.0267351 0.0463066i
\(425\) −13.7980 −0.669299
\(426\) −7.17423 15.5724i −0.347593 0.754485i
\(427\) 0 0
\(428\) 6.00000 + 10.3923i 0.290021 + 0.502331i
\(429\) 16.8990 + 1.55708i 0.815890 + 0.0751764i
\(430\) −5.00000 8.66025i −0.241121 0.417635i
\(431\) 3.79796 6.57826i 0.182941 0.316864i −0.759940 0.649994i \(-0.774772\pi\)
0.942881 + 0.333130i \(0.108105\pi\)
\(432\) 5.00000 + 1.41421i 0.240563 + 0.0680414i
\(433\) −11.7980 −0.566974 −0.283487 0.958976i \(-0.591491\pi\)
−0.283487 + 0.958976i \(0.591491\pi\)
\(434\) 0 0
\(435\) 10.0000 14.1421i 0.479463 0.678064i
\(436\) 8.34847 14.4600i 0.399819 0.692507i
\(437\) 7.44949 0.356357
\(438\) −5.00000 0.460702i −0.238909 0.0220132i
\(439\) −21.7980 −1.04036 −0.520180 0.854057i \(-0.674135\pi\)
−0.520180 + 0.854057i \(0.674135\pi\)
\(440\) −6.89898 −0.328896
\(441\) 0 0
\(442\) −9.79796 −0.466041
\(443\) −5.10102 −0.242357 −0.121178 0.992631i \(-0.538667\pi\)
−0.121178 + 0.992631i \(0.538667\pi\)
\(444\) 7.79796 11.0280i 0.370075 0.523365i
\(445\) −24.4949 −1.16117
\(446\) −10.4495 + 18.0990i −0.494798 + 0.857015i
\(447\) −10.3485 0.953512i −0.489466 0.0450996i
\(448\) 0 0
\(449\) −18.5959 −0.877596 −0.438798 0.898586i \(-0.644596\pi\)
−0.438798 + 0.898586i \(0.644596\pi\)
\(450\) 20.3485 + 3.78194i 0.959236 + 0.178282i
\(451\) −9.79796 + 16.9706i −0.461368 + 0.799113i
\(452\) 7.94949 + 13.7689i 0.373913 + 0.647636i
\(453\) 5.00000 7.07107i 0.234920 0.332228i
\(454\) −0.275255 0.476756i −0.0129184 0.0223753i
\(455\) 0 0
\(456\) 7.44949 10.5352i 0.348854 0.493355i
\(457\) 31.4949 1.47327 0.736635 0.676291i \(-0.236414\pi\)
0.736635 + 0.676291i \(0.236414\pi\)
\(458\) −11.6237 + 20.1329i −0.543141 + 0.940748i
\(459\) 7.44949 7.24604i 0.347712 0.338216i
\(460\) −1.72474 2.98735i −0.0804166 0.139286i
\(461\) 10.1742 17.6223i 0.473861 0.820752i −0.525691 0.850676i \(-0.676193\pi\)
0.999552 + 0.0299238i \(0.00952645\pi\)
\(462\) 0 0
\(463\) 12.8485 + 22.2542i 0.597119 + 1.03424i 0.993244 + 0.116044i \(0.0370213\pi\)
−0.396125 + 0.918197i \(0.629645\pi\)
\(464\) −1.44949 + 2.51059i −0.0672909 + 0.116551i
\(465\) 35.6969 + 3.28913i 1.65541 + 0.152530i
\(466\) 3.50000 + 6.06218i 0.162134 + 0.280825i
\(467\) 5.00000 + 8.66025i 0.231372 + 0.400749i 0.958212 0.286058i \(-0.0923451\pi\)
−0.726840 + 0.686807i \(0.759012\pi\)
\(468\) 14.4495 + 2.68556i 0.667928 + 0.124140i
\(469\) 0 0
\(470\) 16.8990 29.2699i 0.779492 1.35012i
\(471\) 4.60102 + 9.98698i 0.212004 + 0.460176i
\(472\) 2.00000 0.0920575
\(473\) −5.79796 −0.266590
\(474\) −5.72474 12.4261i −0.262946 0.570751i
\(475\) 25.6969 44.5084i 1.17906 2.04219i
\(476\) 0 0
\(477\) 1.10102 + 3.11416i 0.0504123 + 0.142587i
\(478\) 6.39898 + 11.0834i 0.292683 + 0.506941i
\(479\) −14.7980 25.6308i −0.676136 1.17110i −0.976135 0.217163i \(-0.930320\pi\)
0.299999 0.953939i \(-0.403013\pi\)
\(480\) −5.94949 0.548188i −0.271556 0.0250213i
\(481\) 19.1010 33.0839i 0.870932 1.50850i
\(482\) −4.44949 7.70674i −0.202669 0.351032i
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) 11.8990 + 20.6096i 0.540305 + 0.935835i
\(486\) −12.9722 + 8.64420i −0.588431 + 0.392109i
\(487\) −11.1969 + 19.3937i −0.507382 + 0.878811i 0.492582 + 0.870266i \(0.336053\pi\)
−0.999963 + 0.00854475i \(0.997280\pi\)
\(488\) −11.4495 −0.518294
\(489\) 0.202041 0.285729i 0.00913661 0.0129211i
\(490\) 0 0
\(491\) 1.89898 + 3.28913i 0.0856997 + 0.148436i 0.905689 0.423942i \(-0.139354\pi\)
−0.819989 + 0.572379i \(0.806021\pi\)
\(492\) −9.79796 + 13.8564i −0.441726 + 0.624695i
\(493\) 2.89898 + 5.02118i 0.130563 + 0.226143i
\(494\) 18.2474 31.6055i 0.820992 1.42200i
\(495\) 13.4495 15.7313i 0.604510 0.707070i
\(496\) −6.00000 −0.269408
\(497\) 0 0
\(498\) −3.44949 0.317837i −0.154575 0.0142426i
\(499\) −16.6969 + 28.9199i −0.747458 + 1.29463i 0.201580 + 0.979472i \(0.435392\pi\)
−0.949038 + 0.315163i \(0.897941\pi\)
\(500\) −6.55051 −0.292948
\(501\) 18.6969 26.4415i 0.835318 1.18132i
\(502\) −12.5505 −0.560157
\(503\) −24.4949 −1.09217 −0.546087 0.837729i \(-0.683883\pi\)
−0.546087 + 0.837729i \(0.683883\pi\)
\(504\) 0 0
\(505\) 25.0000 1.11249
\(506\) −2.00000 −0.0889108
\(507\) 18.9722 + 1.74810i 0.842585 + 0.0776361i
\(508\) −3.00000 −0.133103
\(509\) −8.44949 + 14.6349i −0.374517 + 0.648683i −0.990255 0.139269i \(-0.955525\pi\)
0.615738 + 0.787951i \(0.288858\pi\)
\(510\) −6.89898 + 9.75663i −0.305492 + 0.432031i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 9.50000 + 37.5248i 0.419435 + 1.65676i
\(514\) 13.8990 24.0737i 0.613058 1.06185i
\(515\) −24.1464 41.8228i −1.06402 1.84293i
\(516\) −5.00000 0.460702i −0.220113 0.0202813i
\(517\) −9.79796 16.9706i −0.430914 0.746364i
\(518\) 0 0
\(519\) −9.34847 20.2918i −0.410352 0.890711i
\(520\) −16.8990 −0.741069
\(521\) −19.3485 + 33.5125i −0.847672 + 1.46821i 0.0356087 + 0.999366i \(0.488663\pi\)
−0.883281 + 0.468845i \(0.844670\pi\)
\(522\) −2.89898 8.19955i −0.126885 0.358885i
\(523\) 0.174235 + 0.301783i 0.00761875 + 0.0131961i 0.869810 0.493387i \(-0.164242\pi\)
−0.862191 + 0.506584i \(0.830908\pi\)
\(524\) −6.72474 + 11.6476i −0.293772 + 0.508828i
\(525\) 0 0
\(526\) −8.05051 13.9439i −0.351019 0.607983i
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) −2.00000 + 2.82843i −0.0870388 + 0.123091i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) −1.89898 3.28913i −0.0824864 0.142871i
\(531\) −3.89898 + 4.56048i −0.169201 + 0.197908i
\(532\) 0 0
\(533\) −24.0000 + 41.5692i −1.03956 + 1.80056i
\(534\) −7.10102 + 10.0424i −0.307291 + 0.434575i
\(535\) 41.3939 1.78961
\(536\) −3.10102 −0.133944
\(537\) −15.0000 1.38211i −0.647298 0.0596423i
\(538\) −1.82577 + 3.16232i −0.0787143 + 0.136337i
\(539\) 0 0
\(540\) 12.8485 12.4976i 0.552910 0.537810i
\(541\) −15.2474 26.4094i −0.655539 1.13543i −0.981758 0.190133i \(-0.939108\pi\)
0.326219 0.945294i \(-0.394225\pi\)
\(542\) 8.44949 + 14.6349i 0.362937 + 0.628625i
\(543\) 3.15153 + 6.84072i 0.135245 + 0.293563i
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) −28.7980 49.8795i −1.23357 2.13660i
\(546\) 0 0
\(547\) −15.7980 + 27.3629i −0.675472 + 1.16995i 0.300859 + 0.953669i \(0.402727\pi\)
−0.976331 + 0.216283i \(0.930607\pi\)
\(548\) 5.89898 + 10.2173i 0.251992 + 0.436463i
\(549\) 22.3207 26.1076i 0.952623 1.11424i
\(550\) −6.89898 + 11.9494i −0.294173 + 0.509523i
\(551\) −21.5959 −0.920017
\(552\) −1.72474 0.158919i −0.0734100 0.00676403i
\(553\) 0 0
\(554\) −5.34847 9.26382i −0.227235 0.393582i
\(555\) −19.4949 42.3157i −0.827512 1.79620i
\(556\) 4.72474 + 8.18350i 0.200374 + 0.347058i
\(557\) 1.55051 2.68556i 0.0656972 0.113791i −0.831306 0.555815i \(-0.812406\pi\)
0.897003 + 0.442024i \(0.145740\pi\)
\(558\) 11.6969 13.6814i 0.495171 0.579181i
\(559\) −14.2020 −0.600682
\(560\) 0 0
\(561\) 2.89898 + 6.29253i 0.122395 + 0.265671i
\(562\) 9.50000 16.4545i 0.400733 0.694090i
\(563\) −13.9444 −0.587686 −0.293843 0.955854i \(-0.594934\pi\)
−0.293843 + 0.955854i \(0.594934\pi\)
\(564\) −7.10102 15.4135i −0.299007 0.649025i
\(565\) 54.8434 2.30728
\(566\) 20.5505 0.863802
\(567\) 0 0
\(568\) 9.89898 0.415352
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) −18.6237 40.4247i −0.780062 1.69320i
\(571\) 14.2020 0.594337 0.297168 0.954825i \(-0.403958\pi\)
0.297168 + 0.954825i \(0.403958\pi\)
\(572\) −4.89898 + 8.48528i −0.204837 + 0.354787i
\(573\) −10.0732 21.8649i −0.420815 0.913421i
\(574\) 0 0
\(575\) −6.89898 −0.287707
\(576\) −1.94949 + 2.28024i −0.0812287 + 0.0950100i
\(577\) 11.7980 20.4347i 0.491155 0.850706i −0.508793 0.860889i \(-0.669908\pi\)
0.999948 + 0.0101829i \(0.00324136\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 5.87117 + 12.7440i 0.243998 + 0.529622i
\(580\) 5.00000 + 8.66025i 0.207614 + 0.359597i
\(581\) 0 0
\(582\) 11.8990 + 1.09638i 0.493229 + 0.0454463i
\(583\) −2.20204 −0.0911992
\(584\) 1.44949 2.51059i 0.0599803 0.103889i
\(585\) 32.9444 38.5337i 1.36208 1.59317i
\(586\) 13.6237 + 23.5970i 0.562791 + 0.974782i
\(587\) −9.07321 + 15.7153i −0.374492 + 0.648639i −0.990251 0.139296i \(-0.955516\pi\)
0.615759 + 0.787934i \(0.288849\pi\)
\(588\) 0 0
\(589\) −22.3485 38.7087i −0.920853 1.59496i
\(590\) 3.44949 5.97469i 0.142013 0.245974i
\(591\) 9.20204 + 19.9740i 0.378521 + 0.821619i
\(592\) 3.89898 + 6.75323i 0.160247 + 0.277556i
\(593\) −7.34847 12.7279i −0.301765 0.522673i 0.674770 0.738028i \(-0.264243\pi\)
−0.976536 + 0.215355i \(0.930909\pi\)
\(594\) −2.55051 10.0745i −0.104649 0.413360i
\(595\) 0 0
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) −11.8990 1.09638i −0.486993 0.0448717i
\(598\) −4.89898 −0.200334
\(599\) −14.2020 −0.580280 −0.290140 0.956984i \(-0.593702\pi\)
−0.290140 + 0.956984i \(0.593702\pi\)
\(600\) −6.89898 + 9.75663i −0.281650 + 0.398313i
\(601\) −6.34847 + 10.9959i −0.258959 + 0.448531i −0.965963 0.258679i \(-0.916713\pi\)
0.707004 + 0.707210i \(0.250046\pi\)
\(602\) 0 0
\(603\) 6.04541 7.07107i 0.246188 0.287956i
\(604\) 2.50000 + 4.33013i 0.101724 + 0.176190i
\(605\) −12.0732 20.9114i −0.490846 0.850170i
\(606\) 7.24745 10.2494i 0.294407 0.416355i
\(607\) −4.34847 + 7.53177i −0.176499 + 0.305705i −0.940679 0.339298i \(-0.889811\pi\)
0.764180 + 0.645003i \(0.223144\pi\)
\(608\) 3.72474 + 6.45145i 0.151058 + 0.261641i
\(609\) 0 0
\(610\) −19.7474 + 34.2036i −0.799551 + 1.38486i
\(611\) −24.0000 41.5692i −0.970936 1.68171i
\(612\) 2.00000 + 5.65685i 0.0808452 + 0.228665i
\(613\) −7.34847 + 12.7279i −0.296802 + 0.514076i −0.975402 0.220432i \(-0.929253\pi\)
0.678601 + 0.734508i \(0.262587\pi\)
\(614\) −0.752551 −0.0303705
\(615\) 24.4949 + 53.1687i 0.987730 + 2.14397i
\(616\) 0 0
\(617\) −21.6969 37.5802i −0.873486 1.51292i −0.858367 0.513036i \(-0.828521\pi\)
−0.0151189 0.999886i \(-0.504813\pi\)
\(618\) −24.1464 2.22486i −0.971312 0.0894970i
\(619\) −2.07321 3.59091i −0.0833295 0.144331i 0.821349 0.570426i \(-0.193222\pi\)
−0.904678 + 0.426096i \(0.859889\pi\)
\(620\) −10.3485 + 17.9241i −0.415605 + 0.719848i
\(621\) 3.72474 3.62302i 0.149469 0.145387i
\(622\) −1.30306 −0.0522480
\(623\) 0 0
\(624\) −4.89898 + 6.92820i −0.196116 + 0.277350i
\(625\) 5.94949 10.3048i 0.237980 0.412193i
\(626\) −24.6969 −0.987088
\(627\) −25.6969 2.36773i −1.02624 0.0945578i
\(628\) −6.34847 −0.253332
\(629\) 15.5959 0.621850
\(630\) 0 0
\(631\) 18.1010 0.720590 0.360295 0.932838i \(-0.382676\pi\)
0.360295 + 0.932838i \(0.382676\pi\)
\(632\) 7.89898 0.314205
\(633\) −3.10102 + 4.38551i −0.123255 + 0.174308i
\(634\) −8.69694 −0.345400
\(635\) −5.17423 + 8.96204i −0.205333 + 0.355648i
\(636\) −1.89898 0.174973i −0.0752994 0.00693812i
\(637\) 0 0
\(638\) 5.79796 0.229543
\(639\) −19.2980 + 22.5720i −0.763415 + 0.892936i
\(640\) 1.72474 2.98735i 0.0681765 0.118085i
\(641\) −20.7474 35.9356i −0.819475 1.41937i −0.906070 0.423129i \(-0.860932\pi\)
0.0865947 0.996244i \(-0.472401\pi\)
\(642\) 12.0000 16.9706i 0.473602 0.669775i
\(643\) 9.69694 + 16.7956i 0.382410 + 0.662353i 0.991406 0.130820i \(-0.0417609\pi\)
−0.608996 + 0.793173i \(0.708428\pi\)
\(644\) 0 0
\(645\) −10.0000 + 14.1421i −0.393750 + 0.556846i
\(646\) 14.8990 0.586193
\(647\) −10.6515 + 18.4490i −0.418755 + 0.725305i −0.995815 0.0913973i \(-0.970867\pi\)
0.577060 + 0.816702i \(0.304200\pi\)
\(648\) −1.39898 8.89060i −0.0549571 0.349256i
\(649\) −2.00000 3.46410i −0.0785069 0.135978i
\(650\) −16.8990 + 29.2699i −0.662833 + 1.14806i
\(651\) 0 0
\(652\) 0.101021 + 0.174973i 0.00395627 + 0.00685246i
\(653\) 4.89898 8.48528i 0.191712 0.332055i −0.754106 0.656753i \(-0.771929\pi\)
0.945818 + 0.324698i \(0.105263\pi\)
\(654\) −28.7980 2.65345i −1.12609 0.103758i
\(655\) 23.1969 + 40.1783i 0.906379 + 1.56990i
\(656\) −4.89898 8.48528i −0.191273 0.331295i
\(657\) 2.89898 + 8.19955i 0.113100 + 0.319895i
\(658\) 0 0
\(659\) −2.34847 + 4.06767i −0.0914834 + 0.158454i −0.908136 0.418676i \(-0.862494\pi\)
0.816652 + 0.577130i \(0.195828\pi\)
\(660\) 5.00000 + 10.8530i 0.194625 + 0.422453i
\(661\) −9.44949 −0.367543 −0.183771 0.982969i \(-0.558831\pi\)
−0.183771 + 0.982969i \(0.558831\pi\)
\(662\) −24.6969 −0.959874
\(663\) 7.10102 + 15.4135i 0.275781 + 0.598610i
\(664\) 1.00000 1.73205i 0.0388075 0.0672166i
\(665\) 0 0
\(666\) −23.0000 4.27475i −0.891232 0.165643i
\(667\) 1.44949 + 2.51059i 0.0561245 + 0.0972104i
\(668\) 9.34847 + 16.1920i 0.361703 + 0.626488i
\(669\) 36.0454 + 3.32124i 1.39360 + 0.128406i
\(670\) −5.34847 + 9.26382i −0.206629 + 0.357893i
\(671\) 11.4495 + 19.8311i 0.442003 + 0.765571i
\(672\) 0 0
\(673\) −15.2980 + 26.4968i −0.589693 + 1.02138i 0.404579 + 0.914503i \(0.367418\pi\)
−0.994272 + 0.106875i \(0.965915\pi\)
\(674\) −17.6969 30.6520i −0.681661 1.18067i
\(675\) −8.79796 34.7518i −0.338634 1.33760i
\(676\) −5.50000 + 9.52628i −0.211538 + 0.366395i
\(677\) 14.6969 0.564849 0.282425 0.959289i \(-0.408861\pi\)
0.282425 + 0.959289i \(0.408861\pi\)
\(678\) 15.8990 22.4846i 0.610597 0.863514i
\(679\) 0 0
\(680\) −3.44949 5.97469i −0.132282 0.229119i
\(681\) −0.550510 + 0.778539i −0.0210956 + 0.0298337i
\(682\) 6.00000 + 10.3923i 0.229752 + 0.397942i
\(683\) −16.1010 + 27.8878i −0.616088 + 1.06710i 0.374104 + 0.927387i \(0.377950\pi\)
−0.990193 + 0.139710i \(0.955383\pi\)
\(684\) −21.9722 4.08372i −0.840128 0.156145i
\(685\) 40.6969 1.55495
\(686\) 0 0
\(687\) 40.0959 + 3.69445i 1.52975 + 0.140952i
\(688\) 1.44949 2.51059i 0.0552613 0.0957153i
\(689\) −5.39388 −0.205490
\(690\) −3.44949 + 4.87832i −0.131320 + 0.185714i
\(691\) −6.95459 −0.264565 −0.132283 0.991212i \(-0.542231\pi\)
−0.132283 + 0.991212i \(0.542231\pi\)
\(692\) 12.8990 0.490346
\(693\) 0 0
\(694\) −19.5959 −0.743851
\(695\) 32.5959 1.23643
\(696\) 5.00000 + 0.460702i 0.189525 + 0.0174629i
\(697\) −19.5959 −0.742248
\(698\) 10.4495 18.0990i 0.395519 0.685059i
\(699\) 7.00000 9.89949i 0.264764 0.374433i
\(700\) 0 0
\(701\) 51.3939 1.94112 0.970560 0.240860i \(-0.0774293\pi\)
0.970560 + 0.240860i \(0.0774293\pi\)
\(702\) −6.24745 24.6773i −0.235795 0.931385i
\(703\) −29.0454 + 50.3081i −1.09547 + 1.89741i
\(704\) −1.00000 1.73205i −0.0376889 0.0652791i
\(705\) −58.2929 5.37113i −2.19544 0.202288i
\(706\) −3.00000 5.19615i −0.112906 0.195560i
\(707\) 0 0
\(708\) −1.44949 3.14626i −0.0544752 0.118244i
\(709\) −11.5959 −0.435494 −0.217747 0.976005i \(-0.569871\pi\)
−0.217747 + 0.976005i \(0.569871\pi\)
\(710\) 17.0732 29.5717i 0.640746 1.10981i
\(711\) −15.3990 + 18.0116i −0.577507 + 0.675486i
\(712\) −3.55051 6.14966i −0.133061 0.230468i
\(713\) −3.00000 + 5.19615i −0.112351 + 0.194597i
\(714\) 0 0
\(715\) 16.8990 + 29.2699i 0.631986 + 1.09463i
\(716\) 4.34847 7.53177i 0.162510 0.281475i
\(717\) 12.7980 18.0990i 0.477949 0.675921i
\(718\) −5.39898 9.35131i −0.201488 0.348988i
\(719\) −4.89898 8.48528i −0.182701 0.316448i 0.760098 0.649808i \(-0.225151\pi\)
−0.942799 + 0.333360i \(0.891817\pi\)
\(720\) 3.44949 + 9.75663i 0.128555 + 0.363608i
\(721\) 0 0
\(722\) −18.2474 + 31.6055i −0.679100 + 1.17624i
\(723\) −8.89898 + 12.5851i −0.330957 + 0.468043i
\(724\) −4.34847 −0.161610
\(725\) 20.0000 0.742781
\(726\) −12.0732 1.11243i −0.448079 0.0412862i
\(727\) 20.2474 35.0696i 0.750936 1.30066i −0.196433 0.980517i \(-0.562936\pi\)
0.947369 0.320143i \(-0.103731\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) −5.00000 8.66025i −0.185058 0.320530i
\(731\) −2.89898 5.02118i −0.107223 0.185715i
\(732\) 8.29796 + 18.0116i 0.306701 + 0.665726i
\(733\) −6.27526 + 10.8691i −0.231782 + 0.401458i −0.958333 0.285655i \(-0.907789\pi\)
0.726551 + 0.687113i \(0.241122\pi\)
\(734\) 2.89898 + 5.02118i 0.107003 + 0.185335i
\(735\) 0 0
\(736\) 0.500000 0.866025i 0.0184302 0.0319221i
\(737\) 3.10102 + 5.37113i 0.114228 + 0.197848i
\(738\) 28.8990 + 5.37113i 1.06379 + 0.197714i
\(739\) 12.7980 22.1667i 0.470781 0.815416i −0.528661 0.848833i \(-0.677306\pi\)
0.999441 + 0.0334173i \(0.0106390\pi\)
\(740\) 26.8990 0.988826
\(741\) −62.9444 5.79972i −2.31232 0.213058i
\(742\) 0 0
\(743\) −18.0000 31.1769i −0.660356 1.14377i −0.980522 0.196409i \(-0.937072\pi\)
0.320166 0.947361i \(-0.396261\pi\)
\(744\) 4.34847 + 9.43879i 0.159423 + 0.346043i
\(745\) −10.3485 17.9241i −0.379139 0.656687i
\(746\) −1.44949 + 2.51059i −0.0530696 + 0.0919192i
\(747\) 2.00000 + 5.65685i 0.0731762 + 0.206973i
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) 4.74745 + 10.3048i 0.173352 + 0.376279i
\(751\) −20.2980 + 35.1571i −0.740683 + 1.28290i 0.211502 + 0.977378i \(0.432165\pi\)
−0.952185 + 0.305523i \(0.901169\pi\)
\(752\) 9.79796 0.357295
\(753\) 9.09592 + 19.7436i 0.331474 + 0.719497i
\(754\) 14.2020 0.517208
\(755\) 17.2474 0.627699
\(756\) 0 0
\(757\) 23.3939 0.850265 0.425132 0.905131i \(-0.360228\pi\)
0.425132 + 0.905131i \(0.360228\pi\)
\(758\) −26.4949 −0.962338
\(759\) 1.44949 + 3.14626i 0.0526131 + 0.114202i
\(760\) 25.6969 0.932126
\(761\) 1.00000 1.73205i 0.0362500 0.0627868i −0.847331 0.531065i \(-0.821792\pi\)
0.883581 + 0.468278i \(0.155125\pi\)
\(762\) 2.17423 + 4.71940i 0.0787642 + 0.170966i
\(763\) 0 0
\(764\) 13.8990 0.502847
\(765\) 20.3485 + 3.78194i 0.735700 + 0.136736i
\(766\) 3.44949 5.97469i 0.124635 0.215874i
\(767\) −4.89898 8.48528i −0.176892 0.306386i
\(768\) −0.724745 1.57313i −0.0261520 0.0567655i
\(769\) 27.0454 + 46.8440i 0.975282 + 1.68924i 0.679000 + 0.734138i \(0.262414\pi\)
0.296282 + 0.955100i \(0.404253\pi\)
\(770\) 0 0
\(771\) −47.9444 4.41761i −1.72667 0.159096i
\(772\) −8.10102 −0.291562
\(773\) −9.97219 + 17.2723i −0.358675 + 0.621243i −0.987740 0.156110i \(-0.950105\pi\)
0.629065 + 0.777353i \(0.283438\pi\)
\(774\) 2.89898 + 8.19955i 0.104202 + 0.294727i
\(775\) 20.6969 + 35.8481i 0.743456 + 1.28770i
\(776\) −3.44949 + 5.97469i −0.123829 + 0.214479i
\(777\) 0 0
\(778\) 7.55051 + 13.0779i 0.270699 + 0.468864i
\(779\) 36.4949 63.2110i 1.30757 2.26477i
\(780\) 12.2474 + 26.5843i